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# Exercise 15 - Chapter 1

edited July 2018

Consider the partition [ [11 12] [13] [21] [22 23] ]

Write down every pair (a, b) such that a ∼ b. There should be 10.

Definition 1.14 Let a, b ∈ A be elements. Given a partition, we define a relation with infix notation ∼, where a ∼ b iff a and b are in the same part.

6 of the pairs are the identities $$(x,x)$$. The other four are due to the partitions with two elements each.
$$(11,11),(12,12),(13,13),(21,21),(22,22),(23,23), \\ (11,12),(12,11), \\ (22,23),(23,22)$$
Comment Source:6 of the pairs are the identities \$$(x,x)\$$. The other four are due to the partitions with two elements each. \$$(11,11),(12,12),(13,13),(21,21),(22,22),(23,23), \\\\ (11,12),(12,11), \\\\ (22,23),(23,22)\$$